The knowledge Base consists of all information about a given domain. The Inference Engine is made up of if-then rules. The knowledge base is regularly updated with new facts which have been deduced using the inference engine.

A classical Expert System may be used in a hospital for diagnosis. The knowledge base would consist of all human symptoms and diseases. The inference engine should consist of rules such

"if the temperature is higher than 38^o then you might have an infection in your body".

Using the inference rules and the information provided by the patient, the expert system should be able to provide correct diagnosis.

Another example comes from the field of theorem proving within Lukasiewicz logic. We have three axioms:

A₁: (A ® (B ® A))

A₂: ((A ® (B ® C)) ® ((A ® B) ® (A ® C)))

A₃: (~A ® ~B) ® (B ® A)

and an inference rule:

Modus-Ponens: A, (A® B) a B.